Mechanics 1 Modelling with Friction Question 11

A chute at a water sports centre has been designed so that swimmers first slide down a steep part which is 10 m long and at an angle of 40° to the horizontal. They then come to a 20 m section with a gentler slope, 11° to the horizontal, where they travel at constant speed.

(i) Find the coefficient of friction between a swimmer and the chute.

(ii) Find the acceleration of a swimmer on the steep part.

(iii) Find the speed at the end of the chute of a swimmer who starts at rest.

(You may assume that no speed is lost at the point where the slope changes.)

An alternative design of chute has the same starting and finishing points but has a constant gradient.

(iv) With what speed do swimmers arrive at the end of this chute?

Solution: